An electric field E given by: E =100 i N/C, for x >0; =-100 i N/C, for x <0 exists in a region. A right circular cylinder of length 10 cm and radius…

\[\begin{aligned} \phi_{L} & =\vec{\mathrm{E}} \cdot \overline{\Delta S} \\ & =100(-\hat{i}) \cdot \Delta S(-\hat{i}) \\ & =100 \times \pi\left(2 \times 10^{-2}\right)^{2} \\ & =4 \pi \times 10^{-2} \mathrm{Nm}^{2} / \mathrm{C} \end{aligned} \] \[\begin{aligned} \phi_{R} & =100(\hat{i}) \cdot \Delta S(\hat{i}) \\ & =100 \times \pi\left(2 \times 10^{-2}\right)^{2} \\ & =4 \pi \times 10^{-2} \mathrm{Nm}^{2} / \mathrm{C} \end{aligned} \] \[\begin{aligned} \phi_{\text {total }} & =\phi_{L}+\phi_{R} \\ & =8 \pi \times 10^{-2} \mathrm{Nm}^{2} / \mathrm{C} \\ & =25.12 \times 10^{-2} \mathrm{Nm}^{2} / \mathrm{C} \end{aligned} \] \[\begin{aligned} \text { Charge } q & =\varepsilon_{0} \phi_{\text {total }} \\ & =25.12 \times 10^{-2} \times 8.85 \times 10^{-12} \\ & =0.22 \times 10^{-11} \mathrm{C} \end{aligned} \]